CN201860122U - Current type multilevel converter applied to wind power synchronization - Google Patents

Current type multilevel converter applied to wind power synchronization Download PDF

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Publication number
CN201860122U
CN201860122U CN201020539268XU CN201020539268U CN201860122U CN 201860122 U CN201860122 U CN 201860122U CN 201020539268X U CN201020539268X U CN 201020539268XU CN 201020539268 U CN201020539268 U CN 201020539268U CN 201860122 U CN201860122 U CN 201860122U
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filter
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马幼捷
刘进华
周雪松
问虎龙
周宣征
刘欣
朱毅然
于阳
谷月
崔立强
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STATE GRID XINYUAN ZHANGJIAKOU SCENERY STORAGE DEMONSTRATION POWER PLANT CO Ltd
State Grid Corp of China SGCC
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Tianjin University of Technology
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    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02BCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/10Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract

The utility model discloses a current type multilevel converter applied to wind power synchronization. The current type multilevel converter is characterized in that the device comprises a main circuit and a control circuit, wherein the main circuit also comprises a rectification circuit and an inverter circuit. The current type multilevel converter has the advantages that that the multilevel converter has the characteristics of large power capacity, low switch frequency, small output harmonic wave and good electromagnetic compatibility and the like, so that the output performance of the converter can be improved while the capacity is increased, and the output current of the current type converter is more easily controlled; therefore, the overcurrent and the short-circuit protection are easy to realize, and the work is more stable and reliable; the direct current inductance has the effect of increasing the voltage, so that the front end power supply voltage is allowed to be lower, therefore, the wind speed scope capable of being used is enlarged; meanwhile, the topology of the current type converter is relatively simple, thereby reducing the cost of the wind power generation system.

Description

Be applied to the current type multi-level convertor assembly of wind-electricity integration
[technical field]
The utility model belongs to wind power-generating grid-connected field, utilizes power electronic technology to design a kind of many level of New type of current type convertor assembly, applies it in the wind power-generating grid-connected system.
[background technology]
Be accompanied by being becoming increasingly acute of the energy and environmental problem, recent two decades comes the research of wind generating technology to obtain unprecedented attention.China is as energy resource consumption big country, and the development speed of China's wind power generation industry is also very fast in recent years.Compare with the conventional power generation usage unit, wind turbine generator has outstanding feature: randomness of (1) wind speed and uncertain decision wind power have randomness and uncertainty; (2) landwid electric field main electrical network of distance and load center are far away, and many with weak local electricity system links; (3) in asynchronous wind driven generator group when operation, is from the electrical network absorbing reactive power.The wind power generation final purpose is to be incorporated into the power networks, put into operation, this characteristics of wind-powered electricity generation itself make its capacity with a low credibility, give electric network active, the reactive balance scheduling brings difficulty, produce power quality problem and voltage stability problem, therefore, the key that electronic power conversion system topological in the wind generator system and control thereof is wind generating technology is incorporated into the power networks, in the last few years, along with improving constantly of power semiconductor technological level, some novel semi-conductor power device such as MCT, IGCT etc. occur in succession, make increasing power electronic equipment be used for large-power occasions and become possibility, for some high pressure, big electric current application scenario, two traditional level converter systems can not satisfy people's demand; And, technological level with the existing power electronic device, be contradiction between its power handling capability and the switching frequency, often power is big more, switching frequency is low more, the appearance of many level converter system technology then can effectively solve the contradiction between the two, difference according to the DC side energy-storage travelling wave tube, many level converter system can be divided into many level of voltage-type converter system and current type multi-level converter system, many level of three-phase electricity flow pattern converter system can be realized the current on line side sineization, and can run on unity power factor, thereby can be used as a kind of unity power factor or High Power Factor commutation system.The current type multi-level converter system is convenient to realize four quadrant running; the easier control of output current; be easy to realize overcurrent and short-circuit protection; advantages such as more stable work is reliable; the current type multi-level converter system has more and more caused people's attention, especially in some specific high-power applications occasion, can directly control output current; characteristics such as the current limiting capacity of circuit own is strong also make it become a kind of very competitive converter system type gradually.
[utility model content]
The utility model purpose is to solve the runnability that how to improve wind-driven generator, the power generating quality of wind-driven generator and the problems such as electrical network compatibility of wind-driven generator, and a kind of current type multi-level convertor assembly that is applied to wind-electricity integration is provided.
The technical solution of the utility model:
The utility model has designed a kind of many level of New type of current type convertor assembly from the thought of converter system " elementary cell parallel connection ", and this device is made up of main circuit and control circuit, and wherein main circuit comprises rectification circuit, inverter circuit and filter.
Rectification circuit: form uncontrollable rectifier bridge by the diode of low price, the alternating current that wind-driven generator is sent is converted to direct current, does not need position or speed probe so in principle, thereby simplified structure, has reduced cost.
Inverter circuit: convert direct current to alternating current, transformer is incorporated into the power networks through being incorporated into the power networks.
Filter: comprise wave filter on AC side and wave filter on DC side; Wave filter on DC side is used for filtering DC side current ripples, will guarantee also that simultaneously there is dynamic responding speed faster in system; Wave filter on AC side is used for the high order harmonic component of filtering inverter circuit output waveform, and making grid-connected current is standard sine wave.
The output of rectification circuit is through inserting the input of inverter circuit behind the filter, the output of inverter circuit is through in parallel with electrical network behind the filter.
Control circuit comprises:
The control system that DSP and FPGA build: the main charge completion signal of dsp chip detects, the duty ratio data computing, and will calculate resulting each phase duty ratio data and be sent in the data latches of FPGA by data/address bus.The function that fpga chip is mainly finished comprises: the first, and adopt counter to produce the multiple row carrier phase shift; The second, the duty ratio data in the data latches are compared with the carrier phase shift generator produces multichannel two logic pwm signals; The 3rd, finish two logic pwm signals to the conversion of three logic pwm signals and the distribution of short circuit pulse.When " resetting " when signal is effective, the whole system initialization; " enable " signal and be used for when system breaks down, blocking fully all PWM outputs.
The output signal of control circuit is connected with the switching tube of forming inverter circuit, and it is played control action.
The inverter circuit of above-mentioned said main circuit adopts the multimode parallel-connection structure, is made up of three three-phases, six switch converter system modules and four shunted resistively inductances.The characteristics of this structure are: the AC side of a plurality of converter system modules is directly in parallel, does not pass through transformer; The DC side of each converter system module is to couple together by shunted resistively inductance; The existence of shunted resistively inductance is divided into several current classes with the DC side total current, provides prerequisite for the main variable flow system exports many current levels.If the DC side of main variable flow system is called prime, AC side is called back level, and the existence of shunted resistively inductance also provides assurance for a level converter system module thereafter participates in a power transfer.
Above-mentioned said wave filter on AC side adopts the LC filter, is mainly used in the high-frequency PWM switch harmonic in the filtering ac-side current, and keeps certain first-harmonic gain.LC filter Mathematical Modeling is:
L di p ( t ) dt + Ri p ( t ) + U cp ( t ) = e p ( t )
C dU cp ( t ) dt = i p ( t ) - i pt ( t )
In the formula, e p(t), i p(t), U Cp(t), i Pt(t) be respectively three-phase electricity flow pattern multi-level rectifying system voltage on line side, current on line side, AC side capacitance voltage and ac-side current; P=a, b, c; L, C, R are respectively the inductance capacitance parameter of AC side LC filter and the equivalent internal resistance of inductance.
Above-mentioned said wave filter on DC side, when the constant current output of three-phase electricity flow pattern multi-level rectifying system, the DC side equivalent electric circuit of three-phase electricity flow pattern multi-level rectifying system can be regarded as the parallel connection of N single module commutation system DC side equivalent electric circuit, its DC side shunted resistively inductance is mainly used in filtering DC side current ripples, will guarantee also that simultaneously there is dynamic responding speed faster in system.
In the above-mentioned said control circuit, Control System Design takes to increase two closed-loop control strategies of load-current feedforward, solved the contradiction between system's open loop amplitude gain spike and the rapidity, even if the system that makes adopts less loop gain, still can have dynamic response and steady-state behaviour faster preferably.System's control principle after the employing load-current feedforward control is the feedfoward control part in the frame of broken lines as shown in Figure 4; G F(S) be the feedfoward control transfer function.As seen from the figure, feedfoward control G F(S) output and outer shroud direct current voltage regulator G Vc(S) output sum is given as the peak value of interior circular current.As long as feedfoward control transfer function G F(S) parameter is selected proper, not only can keep system stability, and can suppress low frequency strong disturbance (as load disturbance), effectively improves the dynamic property of system.
Above-mentioned said FPGA is that (three-phase electricity flow pattern multi-level rectifying system main circuit switch device is more, needs the multi-channel PWM switching signal for Field Programmable Gate Array, FPGA) chip for field programmable gate array; And adopt three logic PWM Digital Implementation methods also to need to carry out some logical operations and handle, obviously, the little process chip of single-chip digital signal (Digital Signal Proeessor, DSP) be difficult to finish design objective, the utility model adopts DSP and FPGA to build the hardware control system platform, has designed the full-digital control system of three-phase electricity flow pattern multi-level rectifying system.
Operation principle of the present utility model:
The operation principle of the current mode converter system that this case is related is: constructed some novel topological structures.The alternating current filter of net side converter system mainly plays the effect of impedance isolation and harmonic wave filter place, and the major parameter that influences filter effect is corner frequency ω nWith damping ratio ξ, select corner frequency f n(f nn/ 2 π) do not have well below system's equivalent switching frequency, this harmonic wave to equivalent switching frequency and near frequency band thereof has the obvious suppression effect, the corner frequency of generally choosing the LC filter be equivalent switch frequently
Figure BSA00000280104100031
Simultaneously, in order to suppress the current on line side vibration, the damping ratio of LC filter must be set also, generally selecting damping ratio to consult is 0.4~0.8, so not only can suppress current oscillation, also can make system have the better dynamic performance.
The method for designing of DC side filtering parameter is the parallel connection of a plurality of single module DC side equivalent electric circuits with the DC side equivalent electric circuit equivalence of multimode commutation system in parallel, therefore when the constant current output of three-phase electricity flow pattern multi-level rectifying system, DC side is presented as first-order system, can require the shunted resistively inductance parameter is designed according to direct current ripple index request and system dynamics response; When the constant voltage output of three-phase electricity flow pattern multi-level rectifying system, can design its DC side shunted resistively inductance parameter and filter capacitor parameter with reference to the Buck circuit theory.
The Digital Implementation principle of the indirect PWM of three logics is at first carrying out nonequivalence operation in twos with three-phase two logic pwm signals, realized generating to three-phase electricity flow pattern converter switches drive signal, not only comprised brachium pontis side switch signal in the new three-phase signal and also comprised brachium pontis side switch signal from the generation of two logic pwm signals.
In the Circuit Design process, the application of two closed loop control methods in three-phase electricity flow pattern multi-level rectifier based on Direct Current Control, take to increase two closed-loop control strategies of load-current feedforward, solved the contradiction between system's open loop amplitude gain spike and the rapidity, even if the system that makes adopts less loop gain, still can have dynamic response and steady-state behaviour faster preferably.
Adopt DSP and FPGA to build the hardware control system platform, the full-digital control system of design three-phase electricity flow pattern multi-level rectifying system, the main charge completion signal of dsp chip detects, the duty ratio data computing, and will calculate resulting each phase duty ratio data and be sent in the data latches of FPGA by data/address bus.The function that fpga chip is mainly finished comprises: the first, and adopt counter to produce the multiple row carrier phase shift; The second, the duty ratio data in the data latches are compared with the carrier phase shift generator produces multichannel two logic pwm signals; The 3rd, finish two logic pwm signals to the conversion of three logic pwm signals and the distribution of short circuit pulse.When " resetting " when signal is effective, the whole system initialization; " enable " signal and be used for when system breaks down, blocking fully all PWM outputs.
Superiority of the present utility model and technique effect are: many level converter system has that power capacity is big, switching frequency is low, output harmonic wave is little and characteristics such as Electro Magnetic Compatibility is good, make converter system when increasing capacity, improve its output performance and become possibility, under rectification state, current type multi-level converter system dc voltage is adjustable, and be lower than supply voltage, present the buck circuit characteristic.In addition, the current type multi-level converter system is used for the motor-driven occasion, and to have a dynamic response fast, can realize regenerative braking and four quadrant running, short-circuit protection reliability advantages of higher.Therefore, the utility model can improve the runnability of wind-driven generator, the power generating quality of wind-driven generator and the electrical network compatibility of wind-driven generator etc., is that wind-electricity integration is more safe and reliable.
[description of drawings]
Fig. 1 wind generator system structure chart that is incorporated into the power networks.
Fig. 2 is many level of multimode parallel-current type converter system.
When Fig. 3 exports for constant current, the equivalent electric circuit of single module converter system DC side, wherein,
L x-DC side shunted resistively inductance,
R x-shunted resistively inductance and circuit equivalent internal resistance,
R LK-load resistance equals NR L
Fig. 4 is the double closed-loop control system schematic diagram after the employing load-current feedforward.
Fig. 5 is many level of three-phase electricity flow pattern converter system digital control platform block diagram.
[embodiment]
Embodiment: a kind of convertor assembly that is applied to the current type multi-level in the wind power-generating grid-connected system, it is characterized in that this system is made up of main circuit and control circuit, wherein main circuit comprises rectification circuit, convertor circuit and filter.
Rectification circuit: form uncontrollable rectifier bridge by the diode of low price, the alternating current that wind-driven generator is sent is converted to direct current, does not need position or speed probe so in principle, thereby simplified structure, has reduced cost.
Inverter circuit: convert direct current to alternating current, transformer is incorporated into the power networks through being incorporated into the power networks.Wherein, also to relate to Filter Design in order to guarantee the quality of power supply.
Filter: comprise wave filter on AC side and wave filter on DC side; Wave filter on DC side is used for filtering DC side current ripples, will guarantee also that simultaneously there is dynamic responding speed faster in system; Wave filter on AC side is used for the high order harmonic component of filtering inverter circuit output waveform, and making grid-connected current is standard sine wave.
Control circuit comprises:
The research of modulation technique: the PWM modulation technique is quite crucial technology in the many level converter system research, and the proposition of it and many level current transformers topological structure is symbiosis.Whether the realization that the PWM modulation technique not only determines many level current transformers and all has direct influence to the output waveform quality of many level current transformers, the minimizing of system loss and the raising of efficient.
The control system that DSP and FPGA build: the main charge completion signal of dsp chip detects, the duty ratio data computing, and will calculate resulting each phase duty ratio data and be sent in the data latches of FPGA by data/address bus.The function that fpga chip is mainly finished comprises: the first, and adopt counter to produce the multiple row carrier phase shift; The second, the duty ratio data in the data latches are compared with the carrier phase shift generator produces multichannel two logic pwm signals; The 3rd, finish two logic pwm signals to the conversion of three logic pwm signals and the distribution of short circuit pulse.When " resetting " when signal is effective, the whole system initialization; " enable " signal and be used for when system breaks down, blocking fully all PWM outputs.
The inverter circuit of above-mentioned said master's circuit adopts multimode parallel-connection structure (see figure 2), and such converter system is made up of a plurality of three-phase six switch converter system modules and several shunted resistively inductances.The characteristics of this structure are: the AC side of a plurality of converter system modules is directly in parallel, does not pass through transformer; The DC side of each converter system module is to couple together by shunted resistively inductance; The existence of shunted resistively inductance is divided into several current classes with the DC side total current, provides prerequisite for the main variable flow system exports many current levels.If the DC side of main variable flow system is called prime, AC side is called back level, and the existence of shunted resistively inductance also provides assurance for a level converter system module thereafter participates in a power transfer.
Above-mentioned said wave filter on AC side adopts the LC filter, is mainly used in the high-frequency PWM switch harmonic in the filtering ac-side current, and keeps certain first-harmonic gain.LC filter Mathematical Modeling is:
L di p ( t ) dt + Ri p ( t ) + U cp ( t ) = e p ( t )
C dU cp ( t ) dt = i p ( t ) - i pt ( t )
In the formula, e p(t), i p(t), U Cp(t), i Pt(t) be respectively three-phase electricity flow pattern multi-level rectifying system voltage on line side, current on line side, AC side capacitance voltage and ac-side current; P=a, b, c; L, C, R are respectively the inductance capacitance parameter of AC side LC filter and the equivalent internal resistance of inductance.
Above-mentioned said wave filter on DC side, according to DC side loadtype difference, there are two kinds of output situations in three-phase electricity flow pattern multi-level rectifying system: constant current output and constant voltage output.When the constant current output of three-phase electricity flow pattern multi-level rectifying system, the DC side equivalent electric circuit (see figure 3) of three-phase electricity flow pattern multi-level rectifying system can be regarded as the parallel connection of N single module commutation system DC side equivalent electric circuit, its DC side shunted resistively inductance is mainly used in filtering DC side current ripples, will guarantee also that simultaneously there is dynamic responding speed faster in system.
Above-mentioned said modulation technique adopts the Digital Implementation method of the indirect PWM of a kind of three logics, this method adopt some simple distances " with " logical operation, realized the totally digitilized technology that generates from the generation of two logic pwm signals to three-phase electricity flow pattern converter system switching drive signal, for the design of many level of three-phase electricity flow pattern converter system numerical control system provides the foundation.
In the above-mentioned said control circuit, Control System Design takes to increase two closed-loop control strategies of load-current feedforward, solved the contradiction between system's open loop amplitude gain spike and the rapidity, even if the system that makes adopts less loop gain, still can have dynamic response and steady-state behaviour faster preferably.Shown in system's control principle (see figure 4) after the employing load-current feedforward control, be the feedfoward control part in the frame of broken lines; G F(S) be the feedfoward control transfer function.As seen from the figure, feedfoward control G F(S) output and outer shroud direct current voltage regulator G Vc(S) output sum is given as the peak value of interior circular current.As long as feedfoward control transfer function G F(S) parameter is selected proper, not only can keep system stability, and can suppress low frequency strong disturbance (as load disturbance), effectively improves the dynamic property of system.
Above-mentioned said FPGA is that (three-phase electricity flow pattern multi-level rectifying system main circuit switch device is more, needs the multi-channel PWM switching signal for Field Programmable Gate Array, FPGA) chip for field programmable gate array; And adopt three logic PWM Digital Implementation methods also to need to carry out some logical operations and handle, obviously, the little process chip of single-chip digital signal (Digital Signal Proeessor, DSP) be difficult to finish design objective, the utility model adopts DSP and FPGA to build the hardware control system platform, has designed the full-digital control system (see figure 5) of three-phase electricity flow pattern multi-level rectifying system.

Claims (5)

1. current type multi-level convertor assembly that is applied to wind-electricity integration is characterized in that this device is made up of main circuit and control circuit, and wherein the composition of main circuit comprises,
Rectification circuit: form uncontrollable rectifier bridge by the diode of low price, the alternating current that wind-driven generator is sent is converted to direct current;
Inverter circuit: convert direct current to alternating current, transformer is incorporated into the power networks through being incorporated into the power networks;
Filter: comprise wave filter on AC side and wave filter on DC side; Wave filter on DC side is used for filtering DC side current ripples, will guarantee also that simultaneously there is dynamic responding speed faster in system; Wave filter on AC side is used for the high order harmonic component of filtering inverter circuit output waveform, and making grid-connected current is standard sine wave;
The output of rectification circuit is through inserting the input of inverter circuit behind the filter, the output of inverter circuit is through in parallel with electrical network behind the filter;
Control circuit comprises:
The control system that DSP and FPGA build: the main charge completion signal of dsp chip detects, the duty ratio data computing, and will calculate resulting each phase duty ratio data and be sent in the data latches of FPGA by data/address bus; The function that fpga chip is mainly finished comprises: the first, and adopt counter to produce the multiple row carrier phase shift; The second, the duty ratio data in the data latches are compared with the carrier phase shift generator produces multichannel two logic pwm signals; The 3rd, finish two logic pwm signals to the conversion of three logic pwm signals and the distribution of short circuit pulse; When " resetting " when signal is effective, the whole system initialization; " enable " signal and be used for when system breaks down, blocking fully all PWM outputs;
The output signal of control circuit is connected with the switching tube of forming inverter circuit, and it is played control action.
2. according to the said current type multi-level convertor assembly of claim 1, it is characterized in that the inverter circuit of this convertor assembly main circuit is made up of three three-phases, six switch converter system modules and four each and every one shunted resistively inductances; The characteristics of this structure are: the AC side of a plurality of converter system modules is directly in parallel, does not pass through transformer; The DC side of each converter system module is to couple together by shunted resistively inductance; The existence of shunted resistively inductance is divided into several current classes with the DC side total current, for main variable flow device output sinusoidal voltage provides prerequisite.
3. according to the said current type multi-level convertor assembly of claim 1, it is characterized in that having used field programmable gate array chip FPGA, FPGA is used for the generation of logical operation and multichannel three logic pwm pulses; When reset signal is effective, the whole system initialization; Enable signal is used for blocking fully all PWM outputs when system breaks down; FPGA mainly comprises carrier phase shift generator, data latching, three two logic pwm signal generators and three three logic pwm signal generators.
4. according to the said current type multi-level convertor assembly of claim 1, it is characterized in that when the constant current of many level of three-phase electricity flow pattern convertor assembly is exported, the DC side equivalent electric circuit of many level of three-phase electricity flow pattern unsteady flow stream device can be regarded as the parallel connection of N single module inverter circuit DC side equivalent electric circuit, its DC side shunted resistively inductance is mainly used in filtering DC side current ripples, will guarantee also that simultaneously there is dynamic responding speed faster in system.
5. according to the said current type multi-level convertor assembly of claim 1, it is characterized in that wave filter on AC side adopts the LC filter, be mainly used in the high order harmonic component in the filtering ac-side current, and keep certain first-harmonic gain; LC filter Mathematical Modeling is:
Figure DEST_PATH_FSB00000454592500021
In the formula, e p(t), i p(t), U Cp(t), i Pt(t) be respectively three-phase electricity flow pattern multi-level rectifying system voltage on line side, current on line side, AC side capacitance voltage and ac-side current p=a, b, c; L, C, R are respectively the inductance capacitance parameter of AC side LC filter and the equivalent internal resistance of inductance.
CN201020539268XU 2010-09-25 2010-09-25 Current type multilevel converter applied to wind power synchronization Expired - Lifetime CN201860122U (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101958653A (en) * 2010-09-25 2011-01-26 天津理工大学 Current-type multi-level converter system for wind power integration
CN110226286B (en) * 2017-01-30 2024-02-02 开利公司 Parallel passive front-end rectifiers with and without interleaving

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101958653A (en) * 2010-09-25 2011-01-26 天津理工大学 Current-type multi-level converter system for wind power integration
CN101958653B (en) * 2010-09-25 2013-05-01 天津理工大学 Current-type multi-level converter system for wind power integration
CN110226286B (en) * 2017-01-30 2024-02-02 开利公司 Parallel passive front-end rectifiers with and without interleaving

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